What is the ruling on someone who vowed to quit social media but forgot the duration of the vow? And what is the ruling on someone who vowed to quit something that brings him enjoyment? And what are the cases in which he must break his vow?

The preponderant view is that a covenant with Allah (mu'ahadat Allah) is considered both an oath (yameen) and a vow (nadhr) if it is undertaken as an act of devotion and obedience (qurbah wa ta'ah). It is considered an oath only if it is undertaken for something that is not an act of devotion. Accordingly, covenanting with Allah to abandon social media is an oath, not a vow. If one returns to using it, an expiation for breaking an oath (kaffarat yameen) is incumbent upon them. Doubt about the intention of the covenant renders it as if there were no intention. In this case, one refers to the reason for the oath. If there is no known reason, then the wording is interpreted based on its Shar'i (Islamic legal) meaning, then its customary meaning, and then its linguistic meaning.